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SUMMARY:Delocalised atoms and electrons in quasi-periodic lattices\, their
  edge modes and interactions with heavy impurities - Dr Manuel Valiente\, 
 Heriot-Watt University
DTSTART:20180301T141500Z
DTEND:20180301T151500Z
UID:TALK101911@talks.cam.ac.uk
CONTACT:21050
DESCRIPTION:The problem of quantum particles in periodic potentials is one
  of the pillars of modern condensed matter physics. For some years now\, a
 toms can be prepared in optical lattices\, and even light in photonic latt
 ices can emulate quantum physics in periodic media under certain condition
 s. In this case\, the single particle problem in the infinite size limit i
 s solved by Bloch's theorem as a consequence of discrete\, rather than con
 tinuous translation symmetry. Even for finite and semi-infinite lattices\,
  Bloch's theorem is easily adapted for bulk states\, while its extension t
 o complex quasi-momenta may be utilised to extract topological edge modes 
 when the system has non-trivial topology -- and these states have very uni
 que properties. \nThe situation drastically changes if the particles move 
 in a superposition of periodic potentials whose periods are incommensurate
  with each other\, i.e. when their ratio is an irrational number: (i) Sinc
 e periodicity is lost\, Bloch's theorem does not apply\; (ii) energy bands
  cannot be defined\, so one cannot in principle decide whether states with
  energies lying within spectral gaps (in the semi-infinite limit) are topo
 logical edge modes\; (iii) the system is inhomogeneous and therefore it is
  unclear whether particle-particle or even potential scattering can happen
  at all\; (iv) there are generally localised and delocalised phases and re
 gions of the spectrum depending. In this talk\, I will consider and give a
  solution to points (i) to (iii) above in the tight-binding approximation 
 and in the delocalised phase. The results I will present are fully general
 \, but will use as an illustration Harper's or Hofstadter's model.
LOCATION:TCM Seminar Room\, Cavendish Laboratory
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